scholarly journals Deriving Weights of Criteria from Inconsistent Fuzzy Comparison Matrices by Using the Nearest Weighted Interval Approximation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohammad Izadikhah
Keyword(s):  
Goal Programming ◽  
Pairwise Comparison ◽  
Programming Method ◽  
Pairwise Comparison Matrix ◽  
Numerical Examples ◽  
Comparison Matrix ◽  
Interval Approximation ◽  
Fuzzy Pairwise Comparison

Deriving the weights of criteria from the pairwise comparison matrix with fuzzy elements is investigated. In the proposed method we first convert each element of the fuzzy comparison matrix into the nearest weighted interval approximation one. Then by using the goal programming method we derive the weights of criteria. The presented method is able to find weights of fuzzy pairwise comparison matrices in any form. We compare the results of the presented method with some of the existing methods. The approach is illustrated by some numerical examples.

A Linear Goal Programming Model for Weight Calculation in Fuzzy AHP and its Application in Product Development

2010 ◽  
Vol 118-120 ◽  
pp. 712-716 ◽  
Author(s):  
Li Jun Yan ◽  
Zong Bin Li ◽  
Xiao Chun Yang
Keyword(s):  
Product Development ◽  
Goal Programming ◽  
Programming Model ◽  
Pairwise Comparison ◽  
Analysis Method ◽  
Pairwise Comparison Matrix ◽  
Wrong Decision ◽  
Comparison Matrix ◽  
Linear Goal Programming ◽  
Goal Programming Model

The key issue of FAHP application is how to derive fuzzy weights from fuzzy pairwise comparison matrix. The most of applications, however, were founding avoiding the use of sophisticated approaches such as fuzzy least squares method and using a simple extent analysis method to derive fuzzy weight from pairwise comparison matrix for the sake of simplicity. But the extent analysis method proves to be incorrect and may lead to a wrong decision result. So, this paper proposes a sound yet simple linear goal programming model to derive weights from pairwise fuzzy comparison matrix, which takes minimizing inconsistence degree of comparison matrix as objective and obtain a normalized weight vector finally. The proposed model is validated by an application to new product development scheme screening decision making.

Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes

2016 ◽  
Vol 33 (03) ◽  
pp. 1650020
Author(s):  
L. N. Pradeep Kumar Rallabandi ◽  
Ravindranath Vandrangi ◽  
Subba Rao Rachakonda
Keyword(s):  
Error Function ◽  
Pairwise Comparison ◽  
Large Set ◽  
Simulation Experiments ◽  
Analytic Hierarchy ◽  
Chi Square ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Hierarchy Process ◽  
Original Information

The analytical hierarchy process (AHP) uses pairwise comparison matrix (PCM) to rank a known set of alternatives. Sometimes the comparisons made by the experts may be inconsistent which results in incorrect weights and rankings for the AHP. In this paper, a method is proposed which identifies inconsistent elements in a PCM and revises them iteratively until the inconsistency is reduced to an acceptable level. An error function similar to chi-square is used to identify the inconsistent elements which are revised with suitable values. The method is illustrated with some numerical examples mentioned in the literature and a comparative study of the results in terms of deviation from the PCM and preservation of original information is taken up. Monte Carlo simulation experiments over a large set of random matrices indicate that the proposed method converges for the moderately inconsistent matrices.

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